Find the limits. lim_{xrightarrow-2} g(f(x)) f(x)=x+7 g(x)=x^2

Find the limits. lim_{xrightarrow-2} g(f(x)) f(x)=x+7 g(x)=x^2

Question
Limits and continuity
asked 2020-11-14
Find the limits. \(\lim_{x\rightarrow-2} g(f(x))\)
\(f(x)=x+7 g(x)=x^2\)

Answers (1)

2020-11-15
Given \(f(x) = x+7\) and \(g(x) = x^2\) ,
To find limit of g(f(x)) first find the expression for g(f(x)) and then apply limit to the resulting expression.
We can g(f(x)) as follow:
\(g(f(x))=g(x+7)\)
\(g(x+7)=(x+7)^2\)
\(=x^2+2(7)(x)+7^2\)
\(=x^2+14x+49\)
Therefore, \(g(f(x))=x^2+14x+49\)
We can the limit for the expression g(f(x)) as follows:
\(\lim_{x\rightarrow-2}g(f(x))=\lim_{x\rightarrow-2}(x^2+14x+49)\)
\(=(-2)^2+14(-2)+49\)
\(=4-28+49=25\)
Therefore \(\lim_{x\rightarrow-2}g(f(x))=25\)
0

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